Download Updated 1-3 Solving Multi

LESSON 1-3
SOLVING MULTI-STEP
EQUATIONS
LEARNING OBJECTIVE(S):
• I CAN SOLVE MULTI-STEP EQUATIONS BY USING THE DISTRIBUTIVE
PROPERTY; COMBINING LIKE TERMS; AND USING INVERSE OPERATIONS.
• I CAN CREATE EQUATIONS
TO REPRESENT REAL -WORLD SITUATIONS.
ESSENTIAL QUESTION: How do I solve Multi-Step Equations?
EX.1: SOLVING MULTI-STEP EQUATIONS
I/WE DO:
STEPS:
Solve each equation.
a.) 2y - 3 = 7
c.) - x + 15 = 12
b.)
𝑥
9
1. Write the original equation.
- 15 = 12
d.) -12 = - 3x - 9
2. Use the Distributive
Property to simplify if needed.
3. Combine like terms to
simplify if needed.
4. Undo Addition or Subtraction
using inverse operations.
5. Undo Multiplication or Division
using inverse operations.
6. Check solution (answer) by
substituting back into the
equation for the variable to see
if it makes the equation true.
EX.1: SOLVING MULTI-STEP EQUATIONS
I/WE DO:
Solve each equation.
e.) 4 −3𝑥 + 1 = −10 𝑥 − 4 − 14𝑥
STEPS:
f.)
1
3
𝑥−4 +
4
−
3
1. Write the original equation.
𝑥 = 6𝑥
2. Use the Distributive Property
to simplify if needed.
3. Combine like terms to
simplify if needed.
4. Undo Addition or Subtraction
using inverse operations.
g.) b) 2 4𝑥 + 3 + 5 = −6 𝑥 − 3 + 10𝑥 − 15
5. Undo Multiplication or
Division using inverseoperations.
6. Check solution (answer) by
substituting back into the
equation for the variable to see
if it makes the equation true.
EX.1: SOLVING MULTI-STEP EQUATIONS
I/WE DO:
STEPS:
Solve each equation.
h.) 2c + c +12= 78
j.) -2(b - 4) = 12
1. Write the original equation.
i.) 3a + 6 + a = 90
k.) 15 = -3(x - 1) + 9
2. Use the Distributive Property to
simplify if needed.
3. Combine like terms to simplify if
needed.
4. Undo Addition or Subtraction
using inverse operations.
5. Undo Multiplication or Division
using inverse operations.
6. Check solution (answer) by
substituting back into the
equation for the variable to see if
it makes the equation true.
EX. 1: SOLVING MULTI-STEP EQUATIONS CONTINUED
YOU DO:
Solve each equation.
l. -2y + 5 + 5y = 14
m. -3z + 8 + (-2z) = -12
n. 13y + 48 = 8y - 47
o. 3x-7(2x -13) = 3 (-2x + 9)
p. m - 5(m - 1) = 7
q. 6(t - 2) = 2(9 – t)
EX. 2: SOLVING A FORMULA FOR ONE OF
ITS VARIABLES.
I/WE DO:
Solve each equation for the indicated variable.
a. Solve for h.
𝟏
𝑨 = 𝒉(𝒃𝟏 + 𝒃𝟐 )
𝟐
b. Solve for 𝒃𝟏 .
𝟏
𝑨 = 𝒉(𝒃𝟏 + 𝒃𝟐 )
𝟐
STEPS:
c. Solve for w.
𝑨 = 𝟐(𝒍𝒘 + 𝒍𝒉 + 𝒘𝒉)
1. Isolate the indicated
variable using inverse
operations.
2. State any restrictions on
appropriate variables.
Solve for x and state any restrictions on appropriate variables.
𝟐𝒙
𝒙
𝒙
f.
𝐝
=
+𝒃
e.
𝒂𝒙
+
𝒃𝒙
−
𝟏𝟓
=
𝟎
d. + 𝟏 =
𝒂
𝒃
𝒂
EX. 2: SOLVING A FORMULA FOR ONE OF
ITS VARIABLES.
YOU DO:
Solve each equation.
g.) Solve for g
𝟏
𝒔 = 𝒈𝒕𝟐
𝟐
STEPS:
h.) Solve for w.
𝑽 = 𝒍𝒘𝒉
i.) Solve for r.
𝑽 = 𝝅𝒓𝟐 𝒉
1. Isolate the indicated
variable using inverse
operations.
2. State any restrictions on
the variable.
Solve for x and state any restrictions on appropriate variables.
j.)
𝒙
𝒂
+𝟏 =
𝒙
𝒃
𝒙
𝒂
k.) + 𝟖 = 𝒃
j.)
𝒙−𝟐
𝟐
=𝒎+𝒏
EX. 3: REAL – WORLD APPLICATION:
I/WE DO:
Answer each problem using the steps provided..
a.) Geometry: The lengths of the sides of a triangle
are in the ratio 3:4:5. The perimeter of the triangle is
18 in. Find the lengths of the sides.
STEPS:
1. Mark the text by doing
the following:
• Circle all of the numbers.
• Underline all of the verbal
phrases that go with each
number you circled.
• Draw a rectangle or box
around the question in the
problem.
2. Define a variable.
3. Write an equation.
4. Solve the Equation.
5. Answer the question in a
complete sentence.
EX. 3: REAL – WORLD APPLICATION:
I/WE DO:
Answer each problem using the steps provided..
b.) Aeronautics: Radar detected an unidentified plane
500 miles away, approaching at 700 mi/hr. Fifteen
minutes later an interceptor plane was dispatched,
traveling at 800 mi/hr. How long did the interceptor
take to reach the approaching plane?
STEPS:
1. Mark the text by doing
the following:
• Circle all of the numbers.
• Underline all of the verbal
phrases that go with each
number you circled.
• Draw a rectangle or box
around the question in the
problem.
2. Define a variable.
3. Write an equation.
4. Solve the Equation.
5. Answer the question in a
complete sentence.
EX. 3: REAL – WORLD APPLICATION:
STEPS:
1. Mark the text by doing
the following:
I/WE DO:
• Circle all of the numbers.
Answer each problem using the steps provided..
• Underline all of the verbal
c.) A dog kennel owner has 100 ft. of fencing to enclose
phrases that go with each
a rectangular dog run. She wants it to be 5 times as
number you circled.
long as it is wide. Find the dimensions of the dog run.
• Draw a rectangle or box
around the question in the
problem.
2. Define a variable.
3. Write an equation.
4. Solve the Equation.
5. Answer the question in a
complete sentence.
EX. 3: REAL – WORLD APPLICATION:
I/WE DO:
Answer each problem using the steps provided..
d.) Two buses leave Fresno at the same time and travel
in opposite directions. One bus averages 55 mph and
the other 45 mph. When will they be 400 miles apart?
Note: distance = (rate)(time) or d=rt
400
55t
STEPS:
1. Mark the text by doing
the following:
• Circle all of the numbers.
• Underline all of the verbal
phrases that go with each
number you circled.
• Draw a rectangle or box
around the question in the
problem.
2. Define a variable.
45t
3. Write an equation.
4. Solve the Equation.
5. Answer the question in a
complete sentence.
EX. 3: REAL – WORLD APPLICATION:
I/WE DO:
Answer each problem using the steps provided..
e.) The sum of three consecutive integers is 90. Find
the three integers.
STEPS:
1. Mark the text by doing
the following:
• Circle all of the numbers.
• Underline all of the verbal
phrases that go with each
number you circled.
• Draw a rectangle or box
around the question in the
problem.
2. Define a variable.
3. Write an equation.
4. Solve the Equation.
5. Answer the question in a
complete sentence.
EX. 3: REAL – WORLD APPLICATION:
YOU DO:
Answer each problem using the steps provided..
f.) Mike and Adam left a bus terminal at the same time
and traveled in opposite directions. Mike’s bus was in
heavy traffic and had to travel 20 mi/h slower than
Adam’s bus. After 3 hours, their buses were 270 miles
apart. How fast was each bus going?
Note: distance = (rate)(time) or d = rt
270
Mike
STEPS:
1. Mark the text by doing
the following:
• Circle all of the numbers.
• Underline all of the verbal
phrases that go with each
number you circled.
• Draw a rectangle or box
around the question in the
problem.
2. Define a variable.
Adam
3. Write an equation.
4. Solve the Equation.
5. Answer the question in a
complete sentence.
EX. 3: REAL – WORLD APPLICATION:
YOU DO:
Answer each problem using the steps provided..
g.) The sides of a triangle are in the ratio 5 : 12 : 13.
What is the length of each side of the triangle if the
perimeter of the triangle is 15 in.?
STEPS:
1. Mark the text by doing
the following:
• Circle all of the numbers.
• Underline all of the verbal
phrases that go with each
number you circled.
• Draw a rectangle or box
around the question in the
problem.
2. Define a variable.
3. Write an equation.
4. Solve the Equation.
5. Answer the question in a
complete sentence.
EX. 3: REAL – WORLD APPLICATION:
STEPS:
1. Mark the text by doing
YOU DO:
the following:
Answer each problem using the steps provided..
• Circle all of the numbers.
h.) Adrian will use part of garage wall as one of the long • Underline all of the verbal
sides of a rectangular rabbit pen. He wants the pen to
phrases that go with each
be 3 times as long as it is wide. He plans to use 68 ft. of
number you circled.
fencing. Find the dimensions of the rabbit pen.
• Draw a rectangle or box
around the question in the
problem.
2. Define a variable.
3. Write an equation.
4. Solve the Equation.
5. Answer the question in a
complete sentence.
EX. 3: REAL – WORLD APPLICATION:
STEPS:
1. Mark the text by doing
YOU DO:
the following:
Answer each problem using the steps provided..
• Circle all of the numbers.
i.) A space probe leaves Earth at the rate of 3km/s. After • Underline all of the verbal
100 days, a radio signal is sent to the probe. Radio
phrases that go with each
5
signals travel at the speed of light, about 3 × 10 km/s.
number you circled.
About how long does the signal take to reach the probe? • Draw a rectangle or box
around the question in the
problem.
2. Define a variable.
3. Write an equation.
4. Solve the Equation.
5. Answer the question in a
complete sentence.
EX. 3: REAL – WORLD APPLICATION:
STEPS:
1. Mark the text by doing
YOU DO:
the following:
Answer each problem using the steps provided..
• Circle all of the numbers.
j.) The sum of four consecutive odd integers is 184. Find • Underline all of the verbal
the four integers.
phrases that go with each
number you circled.
• Draw a rectangle or box
around the question in the
problem.
2. Define a variable.
3. Write an equation.
4. Solve the Equation.
5. Answer the question in a
complete sentence.